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Singular behavior of eigenstates in Anderson's model of localization
1Department of Electrical Engineering, Princeton University, New Jersey 08544, USA.
Physical Review Letters
|September 26, 2012
Summary
Researchers observed a new singularity in the Anderson model of localization with bounded disorder, distinct from the known mobility edge. Numerical calculations in dimensions 1, 2, and 3 reveal richer model behavior than previously understood.
Area of Science:
- Condensed matter physics
- Disordered systems
- Quantum mechanics
Background:
- The Anderson model describes electron localization in disordered materials.
- A well-established phenomenon is the mobility edge, a transition between localized and delocalized states in dimensions greater than two.
- Bounded diagonal disorder introduces unique electronic properties.
Purpose of the Study:
- To investigate an apparent singularity in the Anderson model with bounded diagonal disorder.
- To distinguish this singularity from the established mobility edge.
- To explore the behavior of the Anderson model in dimensions 1, 2, and 3 under uniform on-site disorder.
Main Methods:
- Numerical calculations of the Anderson model.
- Analysis of Anderson's uniform (box) distribution of on-site disorder.
- Contrast of averaged inverse participation ratio and Lyapunov exponent to measure electronic wave function localization length.
Main Results:
- An apparent singularity in electronic properties was observed, distinct from the mobility edge.
- This behavior was studied in dimensions d=1, 2, and 3.
- The evolution of localization length with disorder was analyzed using two different measures.
Conclusions:
- The Anderson model with bounded diagonal disorder exhibits richer behavior than previously established.
- A novel singularity, separate from the mobility edge, appears to exist.
- Further investigation is warranted to fully understand this complex behavior.
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